A056956 Numbers n such that 6n+1 and 6n+5 are both primes.

1, 2, 3, 6, 7, 11, 13, 16, 17, 18, 21, 27, 32, 37, 38, 46, 51, 52, 58, 63, 66, 73, 76, 77, 81, 83, 102, 107, 112, 123, 126, 128, 137, 142, 143, 146, 147, 151, 156, 161, 168, 181, 182, 202, 213, 216, 217, 237, 238, 241, 247, 248, 258, 261, 263, 266, 268, 277, 282

Offset: 1

Author

Henry Bottomley, Jul 18 2000

Keywords

• nonn

Comments

Note that if prime p>3 then p mod 6 = 1 or 5.

Examples

			a(2)=2 since 6*2+1=13 and 6*2+5=17 are both prime.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A002822, A024898, A024899, A059325.

Programs

Mathematica

Select[Range[300], And @@ PrimeQ /@ ({1, 5} + 6#) &] (* Ray Chandler, Jun 29 2008 *)

PARI

is(n)=isprime(n*6+1)&&isprime(n*6+5) \\ M. F. Hasler, Apr 05 2017

Formula

a(n) = (A023200(n+1)-1)/6 = (A046132(n+1)-5)/6 = A047847(n+1)/3

a(n) = floor(A087679(n+1)/6). - M. F. Hasler, Apr 05 2017

Extensions

Edited by N. J. A. Sloane, Nov 07 2006